$\frac{1}{2} \sin ^2 x$

$\frac{1}{2} \cos ^2 x$

$-\frac{1}{2} \cos 2 x$

$-\frac{1}{2} \sin 2 x$

$\frac{x}{2} \sqrt{25 x^2+9}+\frac{11}{10} \sinh ^{-1}\left(\frac{5 x}{3}\right)+C$

$\frac{x}{2} \sqrt{25 x^2+9}-\frac{7}{10} \log \left(\frac{5 x+\sqrt{25 x^2+9}}{3}\right)+C$

$\frac{x}{2} \sqrt{25 x^2+9}+\frac{7}{10} \sinh ^{-1}\left(\frac{5 x}{3}\right)+C$

$\frac{x}{2} \sqrt{25 x^2+9}+\frac{11}{10} \log \left(\frac{5 x-\sqrt{25 x^2+9}}{3}\right)+C$

$\frac{x^{m+1}}{m+1}(\log x)^n-\frac{n}{m+1} I_{m, n-1}$

$\frac{x^m}{m}(\log x)^n-\frac{n-1}{m+1} I_{m+1, n-1}$

$\frac{x^{m+1}}{m} \frac{(\log x)^{n+1}}{n+1}-\frac{n}{m+1} I_{m, n-1}$

$x^m \frac{(\log x)^{n+1}}{n+1}-\frac{n}{m+1} I_{m, n-1}$

1

2

$\frac{3}{4}$

$\frac{1}{2}$